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# The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer

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Math Expert
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Posts: 55277
The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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27 Jul 2018, 01:23
00:00

Difficulty:

35% (medium)

Question Stats:

70% (01:49) correct 30% (01:59) wrong based on 190 sessions

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The sequence S is defined by $$S_n = S_{n - 1} + S_{n - 2} - 1$$ for each integer n ≥ 3. If $$S_1 = 11$$ and $$S_3 = 10$$, what is the value of $$S_5$$?

(A) 0
(B) 9
(C) 10
(D) 18
(E) 19

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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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27 Jul 2018, 02:00
Sn = Sn−1 + Sn−2 − 1
S1=11 and S3=10, S5 = ?

S3 = S2 + S1 − 1
10 = S2 + 11 - 1
S2 = 0

S4 = S3 + S2 − 1
S4 = 10 + 0 - 1 = 9

S5 = S4 + S3 − 1
S5 = 9 + 11 - 1 = 19

Hence, E.
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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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28 Aug 2018, 07:49
1
10=S2+11-1,S2=0

S5=(S4)+S3-1=(S3+S2-1)+S3-1=10+10+0-1-1=18
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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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25 Oct 2018, 15:59
1
Bunuel wrote:
The sequence S is defined by $$S_n = S_{n - 1} + S{n - 2} - 1$$ for each integer n ≥ 3. If $$S_1 = 11$$ and $$S_3 = 10$$, what is the value of $$S_5$$?

(A) 0
(B) 9
(C) 10
(D) 18
(E) 19

Bunuel Could you please format the equation properly? It's currently confusing. Thanks!

$$S_n = S_{n - 1} + S{n - 2} - 1$$ —> $$S_n = S_{n - 1} + S_{n - 2} - 1$$
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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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25 Oct 2018, 21:12
dabaobao wrote:
Bunuel wrote:
The sequence S is defined by $$S_n = S_{n - 1} + S{n - 2} - 1$$ for each integer n ≥ 3. If $$S_1 = 11$$ and $$S_3 = 10$$, what is the value of $$S_5$$?

(A) 0
(B) 9
(C) 10
(D) 18
(E) 19

Bunuel Could you please format the equation properly? It's currently confusing. Thanks!

$$S_n = S_{n - 1} + S{n - 2} - 1$$ —> $$S_n = S_{n - 1} + S_{n - 2} - 1$$

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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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26 Oct 2018, 17:24
Strategy: Utilize a Table for the sequence to help understand how the sequence works

Given
s1 = 11
s3 = 10 = s2 + s1 - 1

Question
s5 = ?

Equations used
sn = s(n-1) + s(n-2) + 1

Calculations
s5 = s4 + s3 - 1
s5 = s4 + 11 - 1
What is s4?

s4 = s3 + s2 - 1
s4 = 11 + s2 - 1
To find s4, we need to know what s2 is

From the Given:
s3 = s2 + s1 - 1
s3 - s1 + 1 = s2
10 - 11 + 1 = s2
0 = s2

s4 = s3 + s2 -1
s4 = 10 + 0 - 1
s4 = 9

s5 = s4 + s3 - 1
s5 = 9 + 10 - 1
s5 = 18
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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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26 Oct 2018, 18:43
Bunuel wrote:
The sequence S is defined by $$S_n = S_{n - 1} + S_{n - 2} - 1$$ for each integer n ≥ 3. If $$S_1 = 11$$ and $$S_3 = 10$$, what is the value of $$S_5$$?

(A) 0
(B) 9
(C) 10
(D) 18
(E) 19

Steps:
1) Compute S_2 = S_3 - S_1 + 1 = 0
2) Using the same method, compute S_4 = 10 - 1 = 9
3)Now, compute S_5 = 9 + 10 - 1 = 18

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The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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21 Jan 2019, 21:56
Good night Bunuel !

I am trying to understand this problem but still do not get it, why are we assuming that S1 + S2 will be equal to S3?

Does this mean that every integer after the last one is going to be -1 from the sum of the las two? I think my main problem is that I am not understanding the wording well enough.

$$S_n = S_{n - 1} + S_{n - 2} - 1$$

Kind regards!
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Posts: 55277
Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer  [#permalink]

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21 Jan 2019, 23:04
jfranciscocuencag wrote:
Good night Bunuel !

I am trying to understand this problem but still do not get it, why are we assuming that S1 + S2 will be equal to S3?

Does this mean that every integer after the last one is going to be -1 from the sum of the las two? I think my main problem is that I am not understanding the wording well enough.

$$S_n = S_{n - 1} + S_{n - 2} - 1$$

Kind regards!

We are told that the sequence S is defined by $$S_n = S_{n - 1} + S_{n - 2} - 1$$ for each integer n ≥ 3.

This means that $$S_n = S_{n - 1} + S_{n - 2} - 1$$ is a formula which gives you every term of the sequence starting from 3rd. Look at the formula, it says that $$S_n$$ equals to the sum of two preceding terms, $$S_{n - 1}$$ and $$S_{n - 2}$$, minus 1. For example:

$$S_3 = S_{3 - 1} + S_{3 - 2} - 1=S_{2} + S_{1} - 1$$;
$$S_4 = S_{4 - 1} + S_{4 - 2} - 1=S_{3} + S_{2} - 1$$;
$$S_5 = S_{5 - 1} + S_{5 - 2} - 1=S_{4} + S_{3} - 1$$;
...

For more check the links below.

12. Sequences

For other subjects:
ALL YOU NEED FOR QUANT ! ! !

Hope it helps.
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Re: The sequence S is defined by Sn = Sn – 1 + Sn – 2 – 1 for each integer   [#permalink] 21 Jan 2019, 23:04
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